**Q:1. A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.**

**(a) What is the rms value of current in the circuit?**

**(b) What is the net power consumed over a full cycle ?**

**Sol. (a) rms value of current , I _{v} = E_{v}/R**

**I _{v} = 220/100 = 2.2 A**

**(b)Power consumed , P = I _{v}^{2} R**

**P = (2.2) ^{2} × 100 = 484 W**

**Q:2. (a) The peak voltage of an ac supply is 300 V. What is the rms voltage?**

**(b) The rms value of current in an ac circuit is 10 A. What is the peak current ?**

**Sol. (a) rms voltage , E _{v} = E_{o}/√2 = 300/1.414 = 212.1 V**

**(b) peak current , I _{o} = √2 I_{v} = 1.414 × 10 = 14.14 A**

**Q:3. A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.**

**Sol. Given , L = 0.044 H , E _{v} = 220 V , frequency ν = 50 Hz.**

**Inductive Reactance , X _{L} = ωL = 2πνL**

**rms value of current , I _{v} = E_{v} /X_{L}**

**On putting given values we get ,**

**I _{v} = 15.9 A**

**Q:4. A 60 μF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.**

**Sol. Given , E _{v} = 110 V , frequency ν = 60 Hz , C = 60 μF**

**Capacitive reactance , X _{c} = 1/ωC = 1/2πνC**

**rms value of current , I _{v} = E_{v} /X_{c}**

**On putting the given values , we get**

**I _{v} = 2.49 A**

**Q:5. In Exercises 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.**

**Sol. Power P _{av} = E_{v }I_{v }cosφ**

**For Q.3 (Inductive Circuit) current lags behind the emf by π/2**

**Hence ,P _{av} = E_{v }I_{v }cosφ = 220 × 15.9 × cos90° = 0**

**In Q.4 (pure capacitive circuit ) current leads emf by phase π/2**

**Hence ,P _{av} = E_{v }I_{v }cosφ = E_{v }I_{v }cos90° = 0**